Consider the matrix A=(100210341)A = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 4 & 1 \end{pmatrix}A=123014001. Which statement about the determinant of AkA^kAk is true?
det(Ak)=k\det(A^k) = kdet(Ak)=k
det(Ak)=1\det(A^k) = 1det(Ak)=1
det(Ak)=k⋅det(A)\det(A^k) = k \cdot \det(A)det(Ak)=k⋅det(A)
det(Ak)=0\det(A^k) = 0det(Ak)=0